44 ideas
| 2056 | Philosophers are always switching direction to something more interesting [Plato] |
| Full Idea: Philosophers are always ready to change direction, if a topic crops up which is more attractive than the one to hand. | |
| From: Plato (Theaetetus [c.368 BCE], 172d) | |
| A reaction: Which sounds trivial, but it may be what God does. |
| 2086 | Understanding mainly involves knowing the elements, not their combinations [Plato] |
| Full Idea: A perfect grasp of any subject depends far more on knowing elements than on knowing complexes. | |
| From: Plato (Theaetetus [c.368 BCE], 206b) |
| 2083 | Either a syllable is its letters (making parts as knowable as whole) or it isn't (meaning it has no parts) [Plato] |
| Full Idea: Either a syllable is not the same as its letters, in which case it cannot have the letters as parts of itself, or it is the same as its letters, in which case these basic elements are just as knowable as it is. | |
| From: Plato (Theaetetus [c.368 BCE], 205b) |
| 2082 | A rational account is essentially a weaving together of things with names [Plato] |
| Full Idea: Just as primary elements are woven together, so their names may be woven together to produce a spoken account, because an account is essentially a weaving together of names. | |
| From: Plato (Theaetetus [c.368 BCE], 202b) | |
| A reaction: If justification requires 'logos', and logos is a 'weaving together of names', then Plato might be taken as endorsing the coherence account of justification. Or do the two 'weavings' correspond? |
| 2052 | Eristic discussion is aggressive, but dialectic aims to help one's companions in discussion [Plato] |
| Full Idea: Eristic discussions involve as many tricks and traps as possible, but dialectical discussions involve being serious and correcting the interlocutor's mistakes only when they are his own fault or the result of past conditioning. | |
| From: Plato (Theaetetus [c.368 BCE], 167e) |
| 15527 | Defining terms either enables elimination, or shows that they don't require elimination [Lewis] |
| Full Idea: To define theoretical terms might be to show how to do without them, but it is better to say that it shows there is no good reason to want to do without them. | |
| From: David Lewis (How to Define Theoretical Terms [1970], Intro) |
| 15854 | A primary element has only a name, and no logos, but complexes have an account, by weaving the names [Plato] |
| Full Idea: A primary element cannot be expressed in an account; it can only be named, for a name is all that it has. But with the things composed of these ...just as the elements are woven together, so the names can woven to become an account. | |
| From: Plato (Theaetetus [c.368 BCE], 202b01-3) | |
| A reaction: This is the beginning of what I see as Aristotle's metaphysics, as derived from his epistemology, that is, ontology is what explains, and what we can give an account [logos] of. Aristotle treats this under 'definitions'. |
| 13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
| Full Idea: Peano's axioms are categorical (any two models are isomorphic). Some conclude that the concept of natural number is adequately represented by them, but we cannot identify natural numbers with one rather than another of the isomorphic models. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 11) by Richard Cartwright - Propositions 11 | |
| A reaction: This is a striking anticipation of Benacerraf's famous point about different set theory accounts of numbers, where all models seem to work equally well. Cartwright is saying that others have pointed this out. |
| 18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
| Full Idea: Peano Arithmetic is about any system of entities that satisfies the Peano axioms. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 6.3) by David Bostock - Philosophy of Mathematics 6.3 | |
| A reaction: This doesn't sound like numbers in the fullest sense, since those should facilitate counting objects. '3' should mean that number of rose petals, and not just a position in a well-ordered series. |
| 17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
| Full Idea: Peano's premises are recommended not only by the fact that arithmetic follows from them, but also by their inherent obviousness. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
| Full Idea: Peano Arithmetic cannot derive its own consistency from within itself. But it can be strengthened by adding this consistency statement or by stronger axioms (particularly ones partially expressing soundness). These are known as Reflexion Principles. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 1.2) by Volker Halbach - Axiomatic Theories of Truth (2005 ver) 1.2 |
| 10216 | We master arithmetic by knowing all the numbers in our soul [Plato] |
| Full Idea: It must surely be true that a man who has completely mastered arithmetic knows all numbers? Because there are pieces of knowledge covering all numbers in his soul. | |
| From: Plato (Theaetetus [c.368 BCE], 198b) | |
| A reaction: This clearly views numbers as objects. Expectation of knowing them all is a bit startling! They also appear to be innate in us, and hence they appear to be Forms. See Aristotle's comment in Idea 645. |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
| Full Idea: Peano's premises are not the ultimate logical premises of arithmetic. Simpler premises and simpler primitive ideas are to be had by carrying our analysis on into symbolic logic. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 2060 | There seem to be two sorts of change: alteration and motion [Plato] |
| Full Idea: There are two kinds of change, I think: alteration and motion. | |
| From: Plato (Theaetetus [c.368 BCE], 181d) |
| 2084 | If a word has no parts and has a single identity, it turns out to be the same kind of thing as a letter [Plato] |
| Full Idea: If a complex or a syllable has no parts and is a single identity, hasn't it turned out to be the same kind of thing as an element or letter? | |
| From: Plato (Theaetetus [c.368 BCE], 205d) |
| 15844 | A sum is that from which nothing is lacking, which is a whole [Plato] |
| Full Idea: But this sum now - isn't it just when there is nothing lacking that it is a sum? Yes, necessarily. And won't this very same thing - that from which nothing is lacking - be a whole? | |
| From: Plato (Theaetetus [c.368 BCE], 205a) | |
| A reaction: This seems to be right, be rather too vague and potentially circular to be of much use. What is the criterion for deciding that nothing is lacking? |
| 15843 | The whole can't be the parts, because it would be all of the parts, which is the whole [Plato] |
| Full Idea: The whole does not consist of parts; for it did, it would be all the parts and so would be the sum. | |
| From: Plato (Theaetetus [c.368 BCE], 204e) | |
| A reaction: That is, 'the whole is the sum of its parts' is a tautology! The claim that 'the whole is more than the sum of its parts' gets into similar trouble. See Verity Harte on this. |
| 15530 | A logically determinate name names the same thing in every possible world [Lewis] |
| Full Idea: A logically determinate name is one which names the same thing in every possible world. | |
| From: David Lewis (How to Define Theoretical Terms [1970], III) | |
| A reaction: This appears to be rigid designation, before Kripke introduced the new word. |
| 2080 | Things are only knowable if a rational account (logos) is possible [Plato] |
| Full Idea: Things which are susceptible to a rational account are knowable. | |
| From: Plato (Theaetetus [c.368 BCE], 201d) |
| 16126 | Expertise is knowledge of the whole by means of the parts [Plato] |
| Full Idea: A man has passed from mere judgment to expert knowledge of the being of a wagon when he has done so in virtue of having gone over the whole by means of the elements. | |
| From: Plato (Theaetetus [c.368 BCE], 207c) | |
| A reaction: Plato is emphasising that the expert must know the hundred parts of a wagon, and not just the half dozen main components, but here the point is to go over the whole via the parts, and not just list the parts. |
| 2050 | It is impossible to believe something which is held to be false [Plato] |
| Full Idea: It is impossible to believe something which is not the case. | |
| From: Plato (Theaetetus [c.368 BCE], 167a) |
| 2076 | How can a belief exist if its object doesn't exist? [Plato] |
| Full Idea: If the object of a belief is what is not, the object of this belief is nothing; but if there is no object to a belief, then that is not belief at all. | |
| From: Plato (Theaetetus [c.368 BCE], 189a) |
| 2045 | Perception is infallible, suggesting that it is knowledge [Plato] |
| Full Idea: Perception is always of something that is, and it is infallible, which suggests that it is knowledge. | |
| From: Plato (Theaetetus [c.368 BCE], 152c) |
| 2067 | Our senses could have been separate, but they converge on one mind [Plato] |
| Full Idea: It would be peculiar if each of us were like a Trojan horse, with a whole bunch of senses sitting inside us, rather than that all these perceptions converge onto a single identity (mind, or whatever one ought to call it). | |
| From: Plato (Theaetetus [c.368 BCE], 184d) |
| 2068 | With what physical faculty do we perceive pairs of opposed abstract qualities? [Plato] |
| Full Idea: With what physical faculty do we perceive being and not-being, similarity and dissimilarity, identity and difference, oneness and many, odd and even and other maths, ….fineness and goodness? | |
| From: Plato (Theaetetus [c.368 BCE], 185d) |
| 2078 | You might mistake eleven for twelve in your senses, but not in your mind [Plato] |
| Full Idea: Sight or touch might make someone take eleven for twelve, but he could never form this mistaken belief about the contents of his mind. | |
| From: Plato (Theaetetus [c.368 BCE], 195e) |
| 2069 | Thought must grasp being itself before truth becomes possible [Plato] |
| Full Idea: If you can't apprehend being you can't apprehend truth, and so a thing could not be known. Therefore knowledge is not located in immediate experience but in thinking about it, since the latter makes it possible to grasp being and truth. | |
| From: Plato (Theaetetus [c.368 BCE], 186c) |
| 2089 | An inadequate rational account would still not justify knowledge [Plato] |
| Full Idea: If you don't know which letters belong together in the right syllables…it is possible for true belief to be accompanied by a rational account and still not be entitled to the name of knowledge. | |
| From: Plato (Theaetetus [c.368 BCE], 208b) | |
| A reaction: In each case of justification there is a 'clinching' stage, for which there is never going to be a strict rule. It might be foundational, but equally it might be massive coherence, or no alternative. |
| 2085 | Parts and wholes are either equally knowable or equally unknowable [Plato] |
| Full Idea: Either a syllable and its letters are equally knowable and expressible in a rational account, or they are both equally unknowable and inexpressible. | |
| From: Plato (Theaetetus [c.368 BCE], 205e) | |
| A reaction: Presumably you could explain the syllable by the letters, but not vice versa, but he must mean that the explanation is worthless without the letters being explained too. So all explanation is worthless? |
| 2091 | Without distinguishing marks, how do I know what my beliefs are about? [Plato] |
| Full Idea: If I only have beliefs about Theaetetus when I don't know his distinguishing mark, how on earth were my beliefs about you rather than anyone else? | |
| From: Plato (Theaetetus [c.368 BCE], 209b) | |
| A reaction: This is a rather intellectualist approach to mental activity. Presumably Theaetetus has lots of distinguishing marks, but they are not conscious. Must Socrates know everything? |
| 2087 | A rational account might be seeing an image of one's belief, like a reflection in a mirror [Plato] |
| Full Idea: A rational account might be forming an image of one's belief, as in a mirror or a pond. | |
| From: Plato (Theaetetus [c.368 BCE], 206d) | |
| A reaction: Not promising, since the image is not going to be clearer than the original, or contain any new information. Maybe it would be clarified by being 'framed', instead of drifting in muddle. |
| 2090 | A rational account involves giving an image, or analysis, or giving a differentiating mark [Plato] |
| Full Idea: A third sort of rational account (after giving an image, or analysing elements) is being able to mention some mark which differentiates the object in question ('the sun is the brightest heavenly body'). | |
| From: Plato (Theaetetus [c.368 BCE], 208c) | |
| A reaction: This is Plato's clearest statement of what would be involved in adding the necessary logos to your true belief. An image of it, or an analysis, or an individuation. How about a cause? |
| 2081 | Maybe primary elements can be named, but not receive a rational account [Plato] |
| Full Idea: Maybe the primary elements of which things are composed are not susceptible to rational accounts. Each of them taken by itself can only be named, but nothing further can be said about it. | |
| From: Plato (Theaetetus [c.368 BCE], 201e) | |
| A reaction: This still seems to be more or less the central issue in philosophy - which things should be treated as 'primitive', and which other things are analysed and explained using the primitive tools? |
| 2088 | A rational account of a wagon would mean knowledge of its hundred parts [Plato] |
| Full Idea: In the case of a wagon, we may only have correct belief, but someone who is able to explain what it is by going through its hundred parts has got hold of a rational account. | |
| From: Plato (Theaetetus [c.368 BCE], 207b) | |
| A reaction: A wonderful example. In science, you know smoking correlates with cancer, but you only know it when you know the mechanism, the causal structure. This may be a general truth. |
| 2047 | What evidence can be brought to show whether we are dreaming or not? [Plato] |
| Full Idea: What evidence could be brought if we were asked at this very moment whether we are asleep and are dreaming all our thoughts? | |
| From: Plato (Theaetetus [c.368 BCE], 158b) |
| 2053 | If you claim that all beliefs are true, that includes beliefs opposed to your own [Plato] |
| Full Idea: To say that everyone believes what is the case, is to concede the truth of the oppositions' beliefs; in other words, the person has to concede that he himself is wrong. | |
| From: Plato (Theaetetus [c.368 BCE], 171a) |
| 2059 | How can a relativist form opinions about what will happen in the future? [Plato] |
| Full Idea: Does a relativist have any authority to decide about things which will happen in the future? | |
| From: Plato (Theaetetus [c.368 BCE], 178c) | |
| A reaction: Nice question! It seems commonsense that such speculations are possible, but without a concept of truth they are ridiculous. |
| 2054 | Clearly some people are superior to others when it comes to medicine [Plato] |
| Full Idea: In medicine, at least, most people are not self-sufficient at prescribing and effecting cures for themselves, and here some people are superior to others. | |
| From: Plato (Theaetetus [c.368 BCE], 171e) |
| 15531 | The Ramsey sentence of a theory says that it has at least one realisation [Lewis] |
| Full Idea: The Ramsey sentence of a theory says that it has at least one realisation. | |
| From: David Lewis (How to Define Theoretical Terms [1970], V) |
| 15528 | A Ramsey sentence just asserts that a theory can be realised, without saying by what [Lewis] |
| Full Idea: If we specify a theory with all of its terms, and then replace all of those terms with variables, we can then say that some n-tuples of entities can satisfy this formula. This Ramsey sentence then says the theory is realised, without specifying by what. | |
| From: David Lewis (How to Define Theoretical Terms [1970], II) | |
| A reaction: [I have compressed Lewis, and cut out the symbolism] |
| 15526 | There is a method for defining new scientific terms just using the terms we already understand [Lewis] |
| Full Idea: I contend that there is a general method for defining newly introduced terms in a scientific theory, one which uses only the old terms we understood beforehand. | |
| From: David Lewis (How to Define Theoretical Terms [1970], Intro) | |
| A reaction: Lewis is game is to provide bridge laws for a reductive account of nature, without having to introduce something entirely new to achieve it. The idea of bridge laws in scientific theory is less in favour these days. |
| 15529 | It is better to have one realisation of a theory than many - but it may not always be possible [Lewis] |
| Full Idea: A uniquely realised theory is, other things being equal, certainly more satisfactory than a multiply realised theory. We should insist on unique realisation as a standard of correctness unless it is a standard too high to be met. | |
| From: David Lewis (How to Define Theoretical Terms [1970], III) | |
| A reaction: The point is that rewriting a theory as Ramsey sentences just says there is at least one realisation, and so it doesn't meet the highest standards for scientific theories. The influence of set-theoretic model theory is obvious in this approach. |
| 2058 | God must be the epitome of goodness, and we can only approach a divine state by being as good as possible [Plato] |
| Full Idea: It is impossible for God to be immoral and not to be the acme of morality; and the only way any of us can approximate to God is to become as moral as possible. | |
| From: Plato (Theaetetus [c.368 BCE], 176c) |
| 2057 | There must always be some force of evil ranged against good [Plato] |
| Full Idea: The elimination of evil is impossible, Theodorus; there must always be some force ranged against good. | |
| From: Plato (Theaetetus [c.368 BCE], 176a) |